A COMPARISON OF HOFER'S METRICS ON HAMILTONIAN DIFFEOMORPHISMS AND LAGRANGIAN SUBMANIFOLDS

By Y. Ostrover. 2002

67 citations recorded by the source corpus.

We compare Hofer's geometries on two spaces associated with a closed symplectic manifold (M,ω). The first space is the group of Hamiltonian diffeomorphisms. The second space ℒ consists of all Lagrangian submanifolds of M × M which are exact Lagrangian isotopic to the diagonal. We show that in the case of a closed symplectic manifold with π2(M) = 0, the canonical embedding of Ham(M) into ℒ, f ↦ graph(f) is not an isometric embedding, although it preserves Hofer's length of smooth paths.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45166de7ea1bbc32377d0ab42a0c7a8cc03cdbb9

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In Geometry and Topology

1. R. Leclercq
2. Yong-Geun Oh
3. Michael Usher
4. E. Shelukhin
5. A. Kislev
6. F. Zapolsky
7. O. Cornea
8. P. Biran

In Mathematical Physics

1. R. Leclercq
2. Yong-Geun Oh
3. Michael Usher
4. E. Shelukhin
5. A. Kislev
6. F. Zapolsky
7. O. Cornea
8. P. Biran

Citations in the corpus

• Calabi quasimorphism and quantum homology (2002, unknown): “The restriction of µ̃ on G̃U coincides with the Calabi homomorphism C̃alU for every U ∈ D. Proof: We follow closely the work by Yaron Ostrover [31].”
• Quasi-states and symplectic intersections (2004, unknown): “Ostrover [38] (cf.”
• Spectral invariants in Lagrangian Floer theory (2006, methodology): “We will illustrate this fact via a family of Hamiltonian diffeomorphisms given by Ostrover [17].”
• LECTURES ON FLOER THEORY AND SPECTRAL INVARIANTS OF HAMILTONIAN FLOWS (2006, result): “As illustrated by Ostrover (2003) , this norm is not the same as but smaller than the Hofer norm.”